Details

Time bar (total: 17.5s)

sample161.0ms

Algorithm
intervals
Results
62.0ms78×body1280valid
52.0ms24×body2560valid
18.0ms55×body640valid
6.0ms106×body80valid
6.0ms28×body320valid
3.0ms69×body80nan
2.0ms16×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.2b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.2b
(pow (+ 1.0 (/ i n)) n)
8.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite846.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
289×add-sqr-sqrt
198×*-un-lft-identity
140×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
32×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down pow-exp clear-num *-commutative distribute-lft-out
Counts
4 → 281
Calls
4 calls:
336.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
162.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms
(pow (+ 1.0 (/ i n)) n)
311.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
335.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
227.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
198.0ms
(pow (+ 1.0 (/ i n)) n)
322.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012263285
150013166

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
0.0b
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
1.2b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.2b
(pow (+ 1.0 (/ i n)) n)

rewrite795.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
29×*-un-lft-identity
28×associate-*l*
22×times-frac
19×add-exp-log add-cube-cbrt
18×add-cbrt-cube
12×pow1 difference-of-squares
8×unpow-prod-down
7×prod-exp cbrt-unprod
6×add-log-exp
5×sqr-pow
4×associate-*r* pow-prod-down distribute-lft-out--
3×pow-unpow
2×cbrt-undiv div-exp associate-*l/ *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log associate-*r/ pow-exp flip-- div-inv distribute-lft-out
Counts
4 → 99
Calls
4 calls:
263.0ms
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
347.0ms
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
164.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms
(pow (+ 1.0 (/ i n)) n)

series1.1s

Counts
4 → 12
Calls
4 calls:
353.0ms
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
342.0ms
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
234.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
206.0ms
(pow (+ 1.0 (/ i n)) n)

simplify61.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0533926
12141822
25002815

prune431.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0)))))
0.0b
(* (/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i) n)
0.1b
(* 100.0 (* (/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i) n))
12.2b
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)

rewrite277.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
20×add-exp-log add-cbrt-cube
19×times-frac
16×associate-*l*
11×pow1
9×associate-*r/ add-log-exp
8×frac-add
7×prod-exp cbrt-unprod
6×flip3-+ flip-+ associate-/l/
4×associate-+r+ flip3-- associate-*r* pow-prod-down flip--
3×cbrt-undiv div-exp associate-/r* sum-log associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l/ *-commutative div-inv unswap-sqr
1×+-commutative associate-+l+ frac-2neg clear-num
Counts
4 → 107
Calls
4 calls:
33.0ms
(+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0)))))
81.0ms
(* (/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i) n)
71.0ms
(* 100.0 (* (/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i) n))
88.0ms
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)

series598.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0)))))
181.0ms
(* (/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i) n)
197.0ms
(* 100.0 (* (/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i) n))
132.0ms
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)

simplify90.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
06832080
130651825
250011816

prune690.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 12.2b

localize21.0ms

Local error

Found 4 expressions with local error:

8.2b
(cbrt (* 100.0 (* (/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i) n)))
12.2b
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)
12.2b
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)
12.2b
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×times-frac
18×associate-/l/
13×associate-*r/
12×frac-add
10×add-exp-log add-cbrt-cube
9×flip3-+ associate-/r* flip-+ associate-/l*
6×flip3-- flip--
4×pow1 add-log-exp
3×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×cbrt-prod cbrt-div pow1/3 associate-*l/
Counts
4 → 109
Calls
4 calls:
58.0ms
(cbrt (* 100.0 (* (/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i) n)))
85.0ms
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)
86.0ms
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)
90.0ms
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)

series1.3s

Counts
4 → 12
Calls
4 calls:
909.0ms
(cbrt (* 100.0 (* (/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i) n)))
135.0ms
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)
127.0ms
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)
131.0ms
(/ (+ (+ (* 1.0 i) (* (log 1.0) n)) (* (pow i 2) (- 0.5 (* 0.5 (log 1.0))))) i)

simplify63.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04472168
118372001
250021999

prune1.9s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 12.2b

regimes459.0ms

Accuracy

44.5% (12.9b remaining)

Error of 23.7b against oracle of 10.8b and baseline of 34.1b

bsearch634.0ms

Steps
ItersRangePoint
9
1.4132788863622532e-206
3.299107912687795e-197
1.3264644651248639e-198
9
-5.1582382664008115e-229
-1.4281663542957573e-234
-1.4508071834264677e-234
9
-2.52020065333125e+99
-1.181987030892061e+91
-2.8822367339188696e+97
7
-2.2138820721712034e+132
-9.063407043561957e+130
-2.1887173671760445e+132
8
-7.242891634590126e+196
-1.3129567736428036e+194
-1.6947020516616556e+196

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06262
16262

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.9s961×body2560valid
1.8s2392×body1280valid
555.0ms1679×body640valid
165.0ms829×body320valid
164.0ms3162×body80valid
93.0ms2217×body80nan
55.0ms436×body160valid
20.0ms6×body5120valid